# Two ideal springs oscillating, find amplitude and phase difference between them

Hi, I am repeating first year exams and would really appreciate some help with my study. Just can't seem to get my head around this problem.

## Homework Statement

Consider two identical ideal springs with a mass m attached which are harmonically oscillating out of phase relative to each other, with the spring constant k = 100 N/m and the mass m = 1x10-3 kg.
At the time t0 = +0.1 sec, the displacement of the spring 1 is x1(t0) = 10 mm and the displacement of spring 2 is x2(t0) = 1 mm.
(i) Calculate the value of the amplitude A of each oscillation.
(ii) Calculate the value of the phase-difference ∅ between the two oscillators.

## Homework Equations

ω = $\sqrt{k/m}$
x = Acos(ωt + ∅)
kA2 = mv2 + kx2

## The Attempt at a Solution

So I calculated ω = 316.228 rad/s. In order to find A, I can use either the position equation or the energy equation. But both of these have an unknown variable. I can't seem to figure out how to find one of these. In the case of the equation x = Acos(ωt + ∅), is ∅ included in this as I am given time with the symbol t0? Any help would really be appreciated. Also for part (ii) of the question, I have never solved a question before asking for the phase difference between two objects. Do you just subtract one from the other? Or is there a specific method?
Thanks Related Introductory Physics Homework Help News on Phys.org
are you sure that there is no extra piece of information? It seems a little odd that the question would give you displacements at time = 0.1sec without telling you something about time = 0.

Yep, I have posted the entire question. Does the subscript 0 on the t mean anything?

t0 usually means time zero or initial starting time.

so t0 = 0.1sec or t0 = +0.1sec are both a little odd.

I can't see a way of providing values for A and phi without more information